The physics of synchrotron radiation

Cover......Page 1
Half-title......Page 3
Title......Page 7
Copyright......Page 8
Dedication......Page 9
Contents......Page 11
Preface......Page 19
Acknowledgments......Page 21
Notation......Page 22
Part I Introduction......Page 25
1.2 The opening angle......Page 27
1.3 The spectrum emitted in a long magnet......Page 28
1.4 The spectrum emitted in a short weak magnet......Page 29
1.5 The wave front of synchrotron radiation......Page 30
1.6 The polarization......Page 32
2.2 The particle motion relevant to the retarded potentials......Page 33
2.3 The retarded electromagnetic potentials......Page 35
2.4 The fields of a moving charge......Page 38
2.5 A discussion of the field equations......Page 42
2.6.1 The field of a charge moving with constant velocity......Page 44
2.6.2 The field of a non-relativistic oscillating charge......Page 51
2.7 The near field and the far field......Page 58
2.8.1 The Fourier integral of the field......Page 59
2.8.2 The periodic motion......Page 61
2.8.3 The motion with a periodic velocity......Page 62
3.1 Introduction......Page 64
3.2 The emitted and received powers......Page 65
3.3.1 The transverse acceleration......Page 66
3.3.2 The longitudinal acceleration......Page 69
3.4 The ultra-relativistic case for transverse acceleration......Page 72
3.5 The angular spectral energy and power density......Page 75
Part II Synchrotron radiation......Page 79
4.1 Introduction......Page 81
4.2.1 The particle motion......Page 82
4.2.2 The dipole approximation......Page 83
4.2.3 The relevant motion......Page 85
4.2.4 The ultra-relativistic approximation......Page 86
4.3.1 The Fourier-transformed field......Page 89
4.3.2 The spectral power density of the radiation......Page 91
4.4.1 The radiation field in the time domain......Page 92
4.4.2 The radiated energy and power in the time domain......Page 95
4.4.3 The radiation field in the time and frequency domains......Page 96
4.5.1 The relevant motion......Page 97
4.5.2 The line spectrum of the electric field......Page 98
4.5.3 The power of the line spectrum......Page 101
4.5.4 The relation between the continuous and the line spectra......Page 103
5.2 The total radiated power and energy......Page 105
5.3.1 The general distribution......Page 107
5.3.2 The distribution at low frequencies......Page 109
5.4.1 The general spectrum......Page 113
5.4.4 The spectrum integrated up to a given frequency......Page 116
5.4.5 The integral over all frequencies......Page 117
5.5.1 The angular distribution as a function of frequency......Page 118
5.5.2 The frequency-integrated angular distribution......Page 120
5.6.1 The description of linear and circular polarization......Page 122
5.6.2 The linear polarization......Page 126
5.6.3 The elliptical polarization......Page 129
5.7 The photon distribution......Page 134
Part III Undulator radiation......Page 139
6.1 Introduction......Page 141
6.2 The interference......Page 142
6.3 The undulator radiation as a wave front......Page 144
6.5 The weak undulator in the laboratory and moving frames......Page 145
6.6 The strong undulator in the laboratory and moving frames......Page 147
6.8 Undulators and related devices......Page 148
7.1.1 The equation of motion......Page 150
7.1.2 The approximation for a weak undulator......Page 152
7.1.3 The observation from a large distance......Page 153
7.1.4 The ultra-relativistic approximation......Page 154
7.2.1 The field calculated from the Liénard–Wiechert equation......Page 155
7.2.2 The undulator field as Lorentz-transformed dipole radiation......Page 156
7.2.3 The undulator radiation in the frequency domain......Page 159
7.2.4 A discussion of the weak-undulator radiation field......Page 160
7.3.1 The energy and power radiated in an undulator......Page 162
7.3.2 The angular spectral power distribution......Page 163
7.3.3 The angular power distribution......Page 165
7.3.4 The spectral power distribution......Page 170
7.4.1 The number and energy of photons......Page 172
7.4.3 The angular spectral photon distribution......Page 175
7.4.4 The undulator radiation on the axis......Page 176
8.1.1 The trajectory in the laboratory frame......Page 178
8.1.2 The trajectory in the moving frame......Page 181
8.1.3 The relevant motion in a strong undulator......Page 183
8.2.1 The radiation field......Page 186
8.3.1 The angular spectral power distribution......Page 191
8.3.2 The angular power distribution......Page 192
8.3.4 The power contained in each harmonic......Page 195
8.3.5 The properties of the radiation on the axis......Page 197
8.3.6 The development with respect to K…......Page 201
9.1 The trajectory......Page 205
9.2.1 The radiation obtained with the lienard–Wiechert formula......Page 209
9.3.2 The angular spectral power distribution......Page 211
9.3.3 The angular power distribution......Page 212
9.3.4 The spectral power distribution......Page 213
9.3.6 The degree of circular polarization......Page 214
9.3.7 The on-axis radiation......Page 216
9.4 The radiation field from a strong helical undulator......Page 217
9.5.2 The angular spectral power distribution......Page 221
9.5.4 The spectral density of helical-undulator radiation......Page 222
9.5.5 The on-axis radiation......Page 224
9.5.6 The development with respect to K…......Page 226
10.2 The wavelength shifter......Page 230
10.3 The multipole wiggler......Page 231
11.1.1 Introduction......Page 233
11.1.3 The radiation from weak magnets......Page 234
11.2.2 Qualitative properties of the short-magnet radiation......Page 237
11.3.1 Introduction......Page 239
11.3.2 The undulator of finite length......Page 240
11.3.3 The undulator radiation with amplitude modulation......Page 243
11.3.4 The undulator radiation with Lorentzian modulation......Page 245
11.4 The Compton back scattering and quantum correction......Page 248
Part IV Applications......Page 251
12.1.1 The limitation on resolution caused by diffraction and the depth-of-field effect......Page 253
12.1.2 Diffraction and the depth-of-field effect for SR from long magnets......Page 254
12.1.4 Diffraction and the depth-of-field effect for short-magnet radiation......Page 255
12.2.1 The Fraunhofer diffraction......Page 256
12.2.2 The emittance of a photon beam......Page 259
12.2.3 The diffraction of synchrotron radiation emitted in long magnets......Page 260
12.2.4 The diffraction of undulator radiation......Page 263
12.2.5 The diffraction for the undulator with a Lorentzian profile......Page 266
12.2.6 A comparison of the properties of beams from various sources......Page 267
13.1 Introduction......Page 268
13.1.1 Lattice magnets......Page 269
13.2.1 The particle dynamics over many revolutions......Page 272
13.2.2 The beam with many particles......Page 280
13.2.3 The dispersion......Page 282
13.2.4 The chromatic aberrations and their correction with sextupoles......Page 283
13.2.6 An example: The FODO lattice......Page 285
13.3.1 Introduction......Page 288
13.3.2 The longitudinal focusing – small amplitudes......Page 290
13.3.3 The longitudinal focusing – large amplitudes......Page 292
14.1 The energy loss......Page 295
14.2.1 Introduction......Page 296
14.2.3 The damping of vertical betatron oscillations......Page 298
14.2.4 The damping of horizontal betatron oscillations......Page 300
14.2.5 The sum of the damping rates......Page 302
14.3.1 Introduction......Page 303
14.3.3 The horizontal emittance......Page 304
14.3.4 The vertical emittance......Page 305
14.4 A summary of the effects of radiation on the electron beam......Page 306
14.5 Changing effects of radiation with wiggler magnets......Page 308
15.1.2 The radiation geometry in the case of a large electron emittance......Page 310
15.2.1 The diffraction limit......Page 312
15.2.2 Small-emittance rings......Page 313
15.3 The temporal coherence......Page 314
15.4 Flux and brightness......Page 319
15.5.2 The radiation from protons......Page 320
15.5.3 The radiation from ions......Page 321
A.1 Definitions and developments......Page 324
A.2 Integrals involving Airy functions......Page 325
B.1 General relations......Page 332
B.2 The approximation for large order and arguments......Page 333
B.3 Sums over squares of Bessel functions......Page 334
B.4 Series of Bessel functions......Page 336
C.1 The plane-undulator radiation......Page 337
C.2 The helical-undulator radiation......Page 338
References......Page 340
Index......Page 345